What are "fringeliers"? I recently received a reviewer comment from a journal submission that asked me to

report how I dealt with outliers and fringeliers.

I had not heard of the  term "fringeliers" and when I googled, there were some articles, but no concise definition. So I thought it would be good to have a question like this that could clarify what "fringeliers" are and provide a definition both for myself and future people asking the same question.
 A: Fringeliers appears to be defined as a less extreme kind of outlier. I.e., data on the fringes of the distribution.
For example, were you to define a cutoff for outliers, fringeliers might be operationalised to be those values that are close to either side of the cutoff (e.g., for a 3 SD cutoff, between 2.7 and 3.3 SD from the mean). 
Osborne and Overbay (2008) write the following:

Although definitions vary, an outlier is generally considered to be a
  data point that is far outside the norm for a variable or population
  (e.g., Jarrell, 1994; Rasmussen, 1988; Stevens, 1984). Hawkins (1980)
  described an outlier as an observation that “deviates so much from
  other observations as to arouse suspicions that it was generated by a
  different mechanism” (p. 1). Outliers have also been defined as values
  that are “dubious in the eyes of the researcher” (Dixon, 1950, p. 488)
  and contaminants (Wainer, 1976).

And go on to introduce the term "fringelier" from Wainer (1976)

Wainer (1976) also introduced the concept of the “fringelier,”
  referring to “unusual events which occur more often than seldom” (p.
  286). These points lie near three standard deviations from the mean and hence may have a disproportionately strong influence on parameter estimates, yet are not as obvious or easily identified as ordinary outliers due to their relative proximity to the distribution center.

Some examples:
In some contexts, outliers suggest that the data is invalid. For example, if a man's  height is recorded as 8 foot tall (say 6.5 SD above the mean), this is probably an invalid measurement. In contrast, if someone's height is recorded as 6 foot 10 inches tall (3 SD above the mean - a fringelier), this might be a valid measurement, but equally, it might suggest a problem with measurement as this is pretty rare. The point is that determining whether a value is invalid gets harder, the less extreme the value becomes.
In other contexts, outliers are a concern because they have an excessive influence on parameter estimates, particularly when using standard statistical methods using least squares and so on. Thus, fringeliers may have greater impact than some most cases, but decisions about whether to retain the data or not for modelling purposes may be less clear.
References


*

*Osborne, J. & Overbay, A. (2008). Best practices in data cleaning: how outliers and “fringeliers” can increase error rates and decrease the quality and precision of your results. In Osborne, J. Best practices in quantitative methods (pp. 205-213). Thousand Oaks, CA: SAGE Publications, Inc. doi: 10.4135/9781412995627

*Wainer, H.Robust statistics: A survey and some prescriptions1(4)285-312(1976).

A: I would think that you'd need to consider the frequency of the fringeliers w.r.t. the data points residing below the cutoff.   If the proportion of fringeliers to "valid" data is high (based on some factor(s)), perhaps the cutoff is unrealistically defined.  Imagine you're in a tent, and the only bears in the area are 3 miles away; but there are 500 of them! :)
